Circumferential register of printing machine cylinders, for example cylinders carrying an image to be printed, such as a forme or a plate cylinder of a printing machine, by axially shifting the cylinder upon axially moving a drive wheel with spiral or inclined gears, is known, see for example German Patent 760 685. In the known arrangement, the shaft of the cylinder is retained in the printing machine in a predetermined, fixed position. This means that the cylinder will always be in engagement with other cylinders or rollers of the printing machine, and that the cylinder itself cannot be moved between an engaged or printing position and the release or thrown-off position. In the known arrangement, the only movement which the cylinder can carry out, besides rotation about its shaft axis, is an axial movement of the cylinder with respect to an engaged or counter cylinder, thereby setting or determining the circumferential register of the printing image.